In the following \(L\) denotes a so-called complete Heyting algebra, i.e. a complete lattice which satisfies an additional distributive law. A stratified \(L\)-topology (SL-topology) on a non-void set \(X\) is a family of mappings in \(L^X\) which contains the constant functions and is closed under the formation of finite meets and arbitrary joins. If \(L\) is the unit interval, an SL-topology can be identified with a fuzzy topology, if \(L = \{0,1\}\) with a topology. It is well-known that topologies can be described by convergent filters and a convergence structure associates with each filter on \(X\) a subset of \(X\) subject to certain conditions. The corresponding substitute of a filter for SL-topologies is an SL-filter, which is a mapping from \(L^X\) to \(L\) which satisfies some easy axioms. If \(L = \{0,1\}\), an SL-filter can be identified with a filter. A collection \((q_\alpha)_{\alpha \in L}\), where each \(q_\alpha\) is a mapping from the set of all SL-filters on \(X\) to \(2^X\), is called an SL-convergence structure on \(X\), if it satisfies some natural axioms, in particular \({\mathcal F} \in q_\alpha(x)\) implies \({\mathcal F} \in q_\beta(x)\) for all \(\beta \leq \alpha\). H.R. Fischer constructed the diagonal filter of a family of filters in order to characterize convergence spaces which are derived from a topological space (the so-called topological convergence spaces), and this paper deals with two generalizations of diagonal filters to SL-filters. The authors show that the resulting categories have nice properties. Also they are equivalent if \(L\) is linearly ordered and the authors characterize topological SL-convergence structures for a special class of SL-convergence spaces which they determined by a so-called probabilistic convergence structure. Reviewer's remark: The same subject has also been studied by \textit{G. Jäger} [see e.g.: Quaest. Math. 31, No.~1, 11--25 (2008; Zbl 1168.54005)].